ANTISYMMETRIC

Etymology

Adjective

antisymmetric (not comparable)

(set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y.

   x R y $\backslash (\backslash Leftrightarrow\backslash )$ 'x divides y' for all x, y ∈ N.

(linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof

(of a matrix) Whose transpose equals its negative (i.e, M^T = −M);

(of a tensor) That changes sign when any two indices are interchanged (e.g, T_ijk = -T_jik);

    $\backslash (\backslash textstyle\; T\_S\backslash equiv\backslash frac\{1\}\{2\}(T+T^T)\backslash )$,     $\backslash (\backslash textstyle\; T\_A\backslash equiv\backslash frac\{1\}\{2\}(T-T^T),\backslash )$     (3.47)

(of a bilinear form) For which B(w,v) = -B(v,w).

Synonyms

• (linear algebra): skew-symmetric

Source: Wiktionary

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